1. A self-adaptive six-degree-of-freedom air floatation simulation test bed is characterized in that:

comprises a test bed (1), a lower station mechanism (2) and an upper station mechanism (3);

the lower station mechanism (2) comprises a lower station platform (4), a lifting support (5), a lifting driving mechanism (6), an air floating journal bearing (7), a first air floating plane bearing (8), a first air floating ball bearing (9) and a self-adaptive air floating group (10);

the lifting support (5) is mounted on the lower station platform (4) through an air-floating journal bearing (7), and the air-floating journal bearing (7) has one degree of freedom of movement and one degree of freedom of rotation, so that the lifting support (5) can vertically move relative to the lower station platform (4) and can rotate around a vertical shaft;

the lifting driving mechanism (6) is used for driving the lifting support (5) to vertically move relative to the lower station platform (4);

the first air-bearing plane bearing (8) is arranged between the lifting driving mechanism (6) and the lifting support (5), and the first air-bearing plane bearing (8) has one degree of freedom of rotation, so that the lifting support (5) can rotate around a vertical shaft relative to the lifting driving mechanism (6);

the lifting support (5) is connected with the upper station mechanism (3) through a first air floating ball bearing (9), and the first air floating ball bearing (9) has three rotational degrees of freedom, so that the upper station mechanism (3) can rotate freely relative to the lifting support (5);

the self-adaptive air flotation group (10) is provided with at least three groups and is uniformly arranged at the bottom of the lower station platform (4), and the self-adaptive air flotation group (10) comprises a self-adaptive bracket (11), a second air flotation plane bearing (12) and a second air flotation ball bearing (13);

the second air-floating plane bearing (12) is arranged between the self-adaptive support (11) and the test bed (1), and the second air-floating plane bearing (12) has two moving degrees of freedom, so that the self-adaptive support (11) can move horizontally relative to the test bed (1);

the self-adaptive support (11) is connected with the lower station platform (4) through a second air-floating ball bearing (13), and the second air-floating ball bearing (13) has three rotational degrees of freedom, so that the self-adaptive support (11) can rotate freely relative to the lower station platform (4);

and a compressed air propulsion system is arranged on the station loading mechanism (3).

2. The adaptive six-degree-of-freedom air-flotation simulation test bed according to claim 1, characterized in that: the station descending mechanism further comprises a first air channel (15), and the first air channel (15) is used for providing air for lubricating the air floating journal bearing (7), the first air floating plane bearing (8) and the first air floating ball bearing (9).

3. The adaptive six-degree-of-freedom air-flotation simulation test bed according to claim 2, characterized in that: first air feed module includes first high-pressure gas jar (14) and first air flue (15), install on station platform (4) down in first high-pressure gas jar (14), station platform (4) are down located in first air flue (15), first high-pressure gas jar (14) are connected with air supporting journal bearing (7), first air supporting plane bearing (8), first air supporting ball bearing (9) respectively through first air flue (15).

4. The adaptive six-degree-of-freedom air-flotation simulation test bed according to claim 1, characterized in that: the self-adaptive air floatation group further comprises a second air passage (17), and the second air passage (17) is used for providing air for lubrication for the second air floatation plane bearing (12) and the second air floatation ball bearing (13).

5. The adaptive six-degree-of-freedom air-flotation simulation test bed according to claim 4, characterized in that: the second air supply module comprises a second high-pressure air tank (16) and a second air passage (17), the second high-pressure air tank (16) is installed on the self-adaptive support (11), the second air passage (17) is arranged in the self-adaptive support (11), and the second high-pressure air tank (16) is respectively connected with the second air-floating plane bearing (12) and the second air-floating ball bearing (13) through the second air passage (17).

6. The adaptive six-degree-of-freedom air-flotation simulation test bed according to claim 5, characterized in that: the second high-pressure air tanks (16) are arranged in a plurality and are uniformly distributed along the same circumferential direction.

7. The adaptive six-degree-of-freedom air flotation simulation test bed according to any one of claims 1 to 6, characterized in that: the lifting driving mechanism (6) is a linear motor, the linear motor is installed on the lower station platform (4), a rotor of the linear motor is connected with the supporting plate (18), and the first air-bearing plane bearing (8) is arranged between the supporting plate (18) and the lifting support (5).

8. A rigid body kinematics and rigid body dynamics calculation method of an adaptive six-degree-of-freedom air-bearing simulation test bed according to any one of claims 1 to 7, comprising the following steps:

A. two coordinate systems are established: one is an inertial frame (O) fixed to the ground_w-X_wY_wZ_w) (ii) a The other is a body coordinate system (O)_o-X_oY_oZ_o)；

B. The body coordinate system (O) of the upper working position mechanism (3) is obtained from the orbital kinematics and the orbital dynamics of the three linear variables_o-X_oY_oZ_o) Origin O_oIn an inertial coordinate system (O) of the test stand (1)_w-X_wY_wZ_w) Change in the three coordinate values above;

C. the attitude kinematics and the attitude dynamics determine the relative coordinate system (O) of the upper station mechanism (3) to the body_o-X_oY_oZ_o) Origin O_oThree angles of change.

9. The rigid body kinematics and rigid body dynamics calculation method of the adaptive six-degree-of-freedom air-floating simulation test bed according to claim 8, wherein the concrete steps of the step C comprise:

c1, body coordinate system (O) of upper station mechanism (3)_o-X_oY_oZ_o) Is converted into an inertial coordinate system (O) of the test stand (1) by a coordinate transformation method_w-X_wY_wZ_w) Vector R in (2):

in the above formulaAs a body coordinate system (O)_o-X_oY_oZ_o) In the inertial coordinate system (O)_w-X_wY_wZ_w) A direction cosine matrix (transfer matrix) of (1); p is the body coordinate system (O)_o-X_oY_oZ_o) Origin O_oIn the inertial frame (O)_w-X_wY_wZ_w) The coordinate value of (1);

if the azimuth angles of the two coordinate systems are defined as: pitch angle theta, yaw angle psi and roll angle phi, the transfer matrixWriting is in the form of the product of three elementary rotation matrices:

in the above formula, c and s are respectively the abbreviations of cos and sin, the same applies below;

the six parameters (three origin coordinates and three azimuth angles) of the adaptive six-degree-of-freedom air-flotation simulation test bed are expressed as a single-value continuous function of time, namely, an adaptive six-degree-of-freedom air-flotation simulation test bed kinematic equation:

x is above₀(t),y₀(t),z₀(t) in an inertial frame (O)_w-X_wY_wZ_w) The lower derivative with respect to time is the body coordinate system (O)_o-X_oY_oZ_o) Origin O_oSpeed of

For the attitude motion, the upper station mechanism (3) is connected with a body coordinate system (O) fixedly connected with the upper station mechanism_o-X_oY_oZ_o) Relative inertial frame (O)_w-X_wY_wZ_w) The rotation of the mechanism (3) is finished by Euler angular velocity around three axes respectively, and the vector sum of the Euler angular velocity is the resultant angular velocity of the rotation of the upper station mechanism (3):

wherein ω is_ox，ω_oy，ω_ozThree angular velocity components of the attitude under a body coordinate system;

euler angular velocity component omega under body coordinate system_ox，ω_oy，ω_ozAnd three Euler angular velocitiesThe relationship of (A) is as follows:

inverting the above transformation matrix to convert the Euler angular velocityAttitude angular velocity component omega in body coordinate system_ox，ω_oy，ω_ozTo show that:

c2, the mass center C and the rotation center O of the upper station mechanism (3)_oThe deviation exists between the two, so that the rigid body posture kinematics and the rigid body posture dynamics of the upper station mechanism (3) are divided into two partsThe calculation method after considering the deviation is given:

setting the mass center C and the rotation center O of the upper station mechanism (3)_oDeviation of r_cThe vector from the center of mass C to the origin of the inertial coordinate system isBody coordinate system (O)_o-X_oY_oZ_o) Origin O_oTo the inertial frame (O)_w-X_wY_wZ_w) The vector of origin isThe main vectors of all external forces acting on the upper station mechanism (3) areAll external forces are opposite to the rotation center O_oThe principal moment vector of a point isThe mass of the upper station mechanism (3) is m_AThe mass of the lower station mechanism (2) is m_PThe mass of the whole self-adaptive six-degree-of-freedom air floatation simulation test bed is M;

and analyzing the rigid body model of the upper station mechanism (3), wherein the rigid body model has the following vector relationship:

the orbit dynamic equation of the upper station mechanism (3) is obtained by that the derivative of the momentum of the upper station mechanism (3) to the time is equal to the main vector of the compressed air propulsion system:

the track dynamics formula of the upper station mechanism (3) can be expressed as follows:

in the above formula, F_pResultant of propulsive forces generated for compressed air propulsion systems, F_QThrust G generated by the first air floating ball bearing (9) to the upper station mechanism (3)_AIs the gravity and F borne by the upper station mechanism (3)_dThe working position mechanism (3) is subjected to external interference forces such as pneumatic interference and the like;

go up station mechanism (3) to O_oThe moment of momentum of the point is:

any mass infinitesimal element and the spherical center O of the first air floating ball bearing (9)_oThe following relationships exist between:

then the upper station mechanism (3) is paired with O_oThe moment of momentum of a point can be written as:

wherein the second term is that the upper station mechanism (3) is aligned with the spherical center O of the first air floating ball bearing (9)_oRelative moment of momentum of (a):

after the moment of momentum is derived over time, there are:

according to the definition of the vector cross product:the above formula can be written as:

because the external moment should be equal to the rigid body pair O_oThe derivative of the relative moment of momentum with time plus the rigid body addition moment to the origin, thus from the rigid body dynamic equilibrium formula, there is:

if introducing rigid body, rotating center O in body coordinate system_oTensor matrix J of moment of inertia_b：

The attitude dynamic equation of the upper station mechanism (3) is as follows:

whereinFor external moment, including air propulsion of compressed air propulsion systems (f)₁～f₄) The generated control moment, the gravity center and the rotation center O of the upper station mechanism (3)_oMoments generated by misalignment, aerodynamic damping moments, and eddy currents moments.

Background

Since the 90 s of the 20 th century, a revolutionary technology, a novel modern microsatellite population technology, which is different from the past satellite concept and improves the performance and the viability of the satellite, appears. For example, in recent years, scientists propose a concept of "separated space vehicles (separated space vehicles)" which decomposes an on-orbit service space vehicle into a plurality of small satellite modules with special functions according to functions, and the small satellite modules are physically separated to form a virtual large satellite by formation flight and wireless transmission to complete specific tasks: for example, the large space telescope array is formed and used for searching the geostationary planet suitable for human survival outside the solar system or searching the life object in the space to detect the motion of the near-earth planet; and also can observe other spacecrafts such as satellites, or directly maintain the failed satellites; images of the earth's surface may also be captured, the earth's ice surface or flood changes monitored, and so forth.

The inventor sets the best example at present by taking 143 satellites to lift off in 24 days by a space exploration technology company, namely falcon 9, USA, 1-25 in 2021, and creating the number of satellites which are launched once.

However, in order to realize formation and orbital transfer flight of a small satellite group, a comprehensive simulation parameter test needs to be performed on a satellite measurement and control system on the ground.

In view of the fact that the number of satellites and measurement and control components on the satellites is large, mass measurement (determination of mass center, inertia product and the like) of each satellite, control of a sliding mode structure, formation of a large number of small satellite groups and the like are complex problems and difficult to solve through a mathematical method.

In contrast, in order to achieve this goal, the air-flotation simulation test bed (also called a satellite control system full physical simulation platform) is a specific and effective simulation method in the process of developing spacecrafts such as satellites. During testing, the motion of the multi-axis air-floatation simulation test bed on the air-floatation simulation test bed can approximately simulate the microgravity and zero-friction space motion of the spacecraft in the outer space environment. Compared with mathematical simulation, the air-float simulation test bed for full physical simulation is used as a direct control loop of a spacecraft motion simulator, so that the difficulty that certain parts are difficult to establish an accurate mathematical model is avoided. The performance and impact of these components on the control system will be intuitively and effectively reflected in the simulation test. This is important to verify the correctness of the design of the satellite control system solution, to verify the functionality and performance of the actual control system. The success rate of space flight tasks of NASA in the United states since 1975 is extremely high, which is inseparable from a set of development procedures of a spacecraft control scheme which is insisted with the NASA and is subject to full physical simulation verification by an air floatation simulation test bed and a satellite control product which is subject to semi-physical simulation closed circuit verification.

The ground simulation test of early-stage spacecrafts such as satellites is basically carried out on a static air floatation simulation test bed, and the test bed provides the freedom degree of rotation around three axes to simulate the space attitude motion of the spacecrafts. However, the modern small satellite needs good orbital mobility in space and needs orbital transfer flight many times, so that a dynamic multi-degree-of-freedom air floatation simulation test bed is needed for testing the small satellite to provide more spatial degrees of freedom, including attitude rotation motion degrees and orbital linear motion degrees of freedom.

With the rapid development of aerospace technology, the development and development of three-degree-of-freedom, four-degree-of-freedom, five-degree-of-freedom and even full-degree-of-freedom air floatation simulation test systems are an important indispensable link for researching modern small intelligent agile spacecrafts, and have huge requirements and functions in the aspects of function test, index inspection, simulation operation, fault diagnosis, fault recurrence, processing strategy research and the like of the spacecraft systems.

However, only a five-degree-of-freedom air flotation simulation test system has been reported so far (reference 1), and an air flotation simulation test system capable of providing an omnidirectional (six-degree-of-freedom) air flotation simulation test system is required for maneuvering requirements such as satellite orbital transfer.

More importantly, for the needs of orbit transfer and cluster flight of spacecrafts such as satellites and the like, the air flotation simulation test system needs to perform the orbit transfer test in a large scale range on a large-scale test bed plane, and even a plurality of air flotation simulation test systems perform the orbit transfer test of a cluster system on a ground simulation platform.

For example, as part of the american type planet discovery program, the american space and flight administration jet propulsion laboratory (NASA JPL) is developing a simulation platform (format Control test-FCT, (references 2 and 3) for a ground Formation flight simulator in order to study and simulate a space autonomous Formation flight mission in a ground environment, the simulation platform has a working area of about 156 inches x168 inches, an additional airport area of 40 inches x58 inches, the platform is formed by splicing 14 small metal plates, the surface unevenness is less than 0.001 inches (0.025 mm), the levelness is less than several milliradians, and three air flotation simulation test platforms are provided on the platform to satisfy the spacecraft Formation flight test.

An outdoor air-floating test bed established by the Lawrence Livermore National Lab floats on a smooth track 100-200 meters long through a track air-floating bearing system. Although it can move only in one linear direction, it can truly reproduce the actual maneuvering flight of a small satellite due to the long moving distance, and can provide an experimental test means for improving the navigation maneuverability and more accurate position tracking (reference 4).

The air film thickness of the air-floating plane bearing on the lower station is only about 15 microns, and the inclination is less than 120 micro radians, so that the parallelism between the air-floating plane bearing and the large-scale test bed plane is required to be very strict. If the non-parallelism is too large, one end of the air-floatation plane bearing can collide with the plane of the large-scale test bed on the ground, and the air-floatation performance is lost; and the other end generates air gap oscillation because the air gap is too large. Thus, the parallelism requirements of large-scale floor test bed planes are more stringent as the platform area increases, thereby causing special difficulties and expensive fabrication costs for processing such high-scale floor test bed planes. The unevenness of the platform will also change with time, temperature, humidity, etc. All the factors need the plane air flotation module on the lower station to have a self-adaptive function, and the parallelism between the plane air flotation module and the plane of the test bed with the large ground scale can be automatically adjusted along with errors such as unevenness of the plane of the test bed with the large ground scale.

The patent application CN111024310A of the invention provides a multi-dimensional air flotation follow-up system (reference 5) for satellite high-precision quality measurement, which comprises a spherical air flotation module, a cylindrical air flotation module, a planar air flotation module, a two-axis rotation assembly, an upper platform, a force transmission cylinder, a differential test module, a rack and an air path control system, wherein the spherical air flotation module supports the weight of a measured piece through the upper platform and has three rotational degrees of freedom; the cylindrical air floatation module is used as a radial support to transfer radial load and has freedom degrees of movement and rotation; the force transmission cylinder is arranged between the spherical air flotation module and the cylindrical air flotation module; the biaxial rotation assembly is matched with spherical air floatation to realize the moment balance of any phase, and has pitching and rolling freedom degrees; the planar air floatation module is used for supporting the two-axis rotation assembly, has two translation degrees of freedom and one rotation degree of freedom, and is matched with the two-axis rotation assembly to realize any phase moment balance; the differential test module is used as a force transmission path for spherical hinge moment balance, so that the balance of the pull pressure at any angle in a plane is realized, and the bidirectional pull pressure of two coordinate axes is tested. The two-axis rotation component comprises a rotation inner frame, a rotation outer frame, a first shafting and a second shafting; the cylindrical air floatation module is connected with the rotary inner frame through a first shaft system, so that the cylindrical air floatation module rotates around a Z axis; the rotary inner frame is connected with the rotary outer frame through a second shaft system, so that the rotary inner frame rotates around the Y axis; and two sides of the rotary outer frame are fixedly connected with the sensing support through the tension and compression sensors. However, the two translational degrees of freedom are actually restricted, and can only be used for quality measurement of the satellite, and the physical orbital transfer test cannot be performed on equipment on the satellite.

In addition, orbital transfer tests for small satellites require not only orbital transfer in a plane but also orbital transfer in a vertical direction. Therefore, the test platform as the moonlet measurement and control system needs to have orbital transfer capability in three linear directions.

Therefore, the development of an air floatation simulation test system with self-adaptive capacity and six degrees of freedom is an important content for developing the modern microsatellite group technology.

Reference to the literature

Reference 1, Dae-Min Cho, etc. "A5-dof Experimental Platform for Autonomous space fractional vacuus and packaging", April 2009, DOI:10.25146.2009-1869, AIAA

Reference 2, Regehr Martin W.etc. "The Formation Control test bed", IEEE Aerospace computer Society,2004: 557-.

Reference 3 Sohl Garett A., etc. "Distributed Simulation for formatting flash applications. AIAA2005: 1162-1173.

Reference 4 Ledebohr A.G. "Down-to-Earth Testing of Micro Satellites", Lawrence Livermore National Lab Science & Technology Review, 1998.

Reference 5 CN111024310A, a multidimensional air-float following system for satellite high-precision quality measurement.

Disclosure of Invention

The invention aims to solve the defects of the prior art, and provides a self-adaptive six-degree-of-freedom air floatation simulation test bed which is used for providing a satellite air floatation simulation test with six degrees of freedom for a station loading mechanism and can more comprehensively and truly check the performance of a satellite measurement and control system, particularly the omnibearing orbital transfer performance; the lower station platform is parallel to the test bed in a self-adaptive mode through the self-adaptive air flotation group, so that the processing difficulty of the test bed is greatly reduced, and the possibility of a test with larger scale is provided; and the ground large-scale test bed can adopt a form of unlimited splicing of local small platforms, can meet the test requirement of the ground large-scale test, and provides test conditions for multi-satellite orbital transfer and formation tests.

The technical problem to be solved is realized by adopting the following technical scheme: a self-adaptive six-degree-of-freedom air floatation simulation test bed comprises a test bed, a lower station mechanism and an upper station mechanism;

the lower station mechanism comprises a lower station platform, a lifting support, a lifting driving mechanism, an air floatation journal bearing, a first air floatation plane bearing, a first air floatation ball bearing and a self-adaptive air floatation group;

the lifting support is arranged on the lower station platform through an air-floating journal bearing, and the air-floating journal bearing has a moving degree of freedom and a rotating degree of freedom, so that the lifting support can vertically move relative to the lower station platform and rotate around a vertical shaft;

the lifting driving mechanism is used for driving the lifting support to vertically move relative to the lower working platform;

the first air-bearing plane bearing is arranged between the lifting driving mechanism and the lifting support, and has a rotational degree of freedom, so that the lifting support can rotate around a vertical shaft relative to the lifting driving mechanism;

the lifting support is connected with the station loading mechanism through a first air floating ball bearing, and the first air floating ball bearing has three rotational degrees of freedom, so that the station loading mechanism can rotate freely relative to the lifting support;

the self-adaptive air floatation group is provided with at least three groups and is uniformly arranged at the bottom of the lower station platform, and the self-adaptive air floatation group comprises a self-adaptive bracket, a second air floatation plane bearing and a second air floatation ball bearing;

the second air-floating plane bearing is arranged between the self-adaptive support and the test bed, and has two moving degrees of freedom, so that the self-adaptive support can horizontally move relative to the test bed;

the self-adaptive support is connected with the lower station platform through a second air ball bearing, and the second air ball bearing has three rotational degrees of freedom, so that the self-adaptive support can rotate freely relative to the lower station platform;

and the upper station mechanism is provided with a compressed air propulsion system.

Compared with the prior art, the invention has the beneficial effects that:

(1) in the actual formation flight or obstacle avoidance and orbit change flight of a satellite group with multiple satellites in space, each satellite is required to realize the orbit change flight in six directions. The invention can provide satellite air floatation simulation test with six degrees of freedom (three degrees of freedom of movement and three degrees of freedom of rotation) for the station loading mechanism. Therefore, the performance of the satellite measurement and control system, especially the omnibearing orbital transfer performance, can be more comprehensively and truly checked.

(2) The lower station platform is parallel to the test bed in a self-adaptive mode through the self-adaptive air flotation group, so that the requirement for the unevenness of the whole test bed plane can be decomposed into the requirement for the local unevenness in a differential mode, the processing difficulty of the test bed is greatly reduced, and the possibility is provided for the test with larger size.

(3) The self-adaptive air flotation group can be used for forming a test bed in an infinite splicing mode, so that the test bed with large ground scale can adopt a local small platform infinite splicing mode, as long as each small platform meets the requirements of parallelism and roughness, the transition area formed by splicing the small platforms and the small platforms also meets the requirements of parallelism and roughness of a local area, the test requirement with large ground scale can be met in such a difference mode of 'breaking the whole into zero' and the self-adaptive mode of a lower workstation mechanism, and test conditions are provided for multi-satellite orbital transfer and formation tests.

The technical scheme of the invention is as follows: the station mechanism still includes first air feed module down, first air feed module is used for providing the air that is used for lubricating for air supporting journal bearing, first air supporting plane bearing, first air supporting ball bearing.

The technical scheme of the invention is as follows: the first gas supply module comprises a first high-pressure gas tank and a first gas passage, the first high-pressure gas tank is installed on the lower station platform, the first gas passage is arranged in the lower station platform, and the first high-pressure gas tank is connected with the air floating journal bearing, the first air floating plane bearing and the first air floating ball bearing through the first gas passage.

The technical scheme of the invention is as follows: the self-adaptive air floating group further comprises a second air supply module, and the second air supply module is used for providing air for lubrication for the second air floating plane bearing and the second air floating ball bearing.

The technical scheme of the invention is as follows: the second air supply module comprises a second high-pressure air tank and a second air passage, the second high-pressure air tank is installed on the self-adaptive support, the second air passage is arranged in the self-adaptive support, and the second high-pressure air tank is connected with a second air-floating plane bearing and a second air-floating ball bearing through the second air passage respectively.

The technical scheme of the invention is as follows: the second high-pressure gas tanks are provided with a plurality of high-pressure gas tanks which are uniformly distributed along the same circumferential direction. By adopting the technical scheme, the center of mass of each self-adaptive air floatation group is superposed with the resultant force center of the air buoyancy of the second air floatation plane bearing and is vertically upward.

The technical scheme of the invention is as follows: the lifting driving mechanism is a linear motor, the linear motor is installed on the lower station platform, a rotor of the linear motor is connected with the supporting plate, and the first air-bearing plane bearing is arranged between the supporting plate and the lifting support.

The invention also provides a rigid body kinematics and rigid body dynamics calculation method of the self-adaptive six-degree-of-freedom air floatation simulation test bed, which comprises the following steps:

A. two coordinate systems are established: one is an inertial frame (O) fixed to the ground_w-X_wY_wZ_w) (ii) a The other is a body coordinate system (O)_o-X_oY_oZ_o)；

B. Determining the body coordinate system (O) of the upper working position mechanism from the orbital kinematics and the orbital dynamics of the three linear variables_o-X_oY_oZ_o) Origin O_oInertial frame (O) on test stand_w-X_wY_wZ_w) Change in the three coordinate values above;

C. the relative coordinate system (O) of the upper station mechanism to the body is obtained by attitude kinematics and attitude dynamics_o-X_oY_oZ_o) Origin O_oThree angles of change.

In the technical scheme of the invention, the step C comprises the following specific steps:

c1, body coordinate system (O) of upper station mechanism_o-X_oY_oZ_o) Is converted into an inertial coordinate system (O) of the test bed by a coordinate transformation method_w-X_wY_wZ_w) Vector R in (2):

in the above formulaAs a body coordinate system (O)_o-X_oY_oZ_o) In the inertial coordinate system (O)_w-X_wY_wZ_w) A direction cosine matrix (transfer matrix) of (1); p is the body coordinate system (O)_o-X_oY_oZ_o) Origin O_oIn the inertial frame (O)_w-X_wY_wZ_w) The coordinate value of (1);

if the azimuth angles of the two coordinate systems are defined as: pitch angle theta, yaw angle psi and roll angle phi, the transfer matrixWriting is in the form of the product of three elementary rotation matrices:

in the above formula, c and s are respectively the abbreviations of cos and sin, the same applies below;

the six parameters (three origin coordinates and three azimuth angles) of the adaptive six-degree-of-freedom air-flotation simulation test bed are expressed as a single-value continuous function of time, namely, an adaptive six-degree-of-freedom air-flotation simulation test bed kinematic equation:

x is above₀(t),y₀(t),z₀(t) in an inertial frame (O)_w-X_wY_wZ_w) The lower derivative with respect to time is the body coordinate system (O)_o-X_oY_oZ_o) Origin O_oSpeed of

For the attitude motion, the upper station mechanism (3) is connected with a body coordinate system (O) fixedly connected with the upper station mechanism_o-X_oY_oZ_o) Relative inertial frame (O)_w-X_wY_wZ_w) The rotation of the mechanism (3) is finished by Euler angular velocity around three axes respectively, and the vector sum of the Euler angular velocity is the resultant angular velocity of the rotation of the upper station mechanism (3):

wherein ω is_ox，ω_oy，ω_ozThree angular velocity components of the attitude under a body coordinate system;

euler angular velocity component omega under body coordinate system_ox，ω_oy，ω_ozAnd three Euler angular velocitiesThe relationship of (A) is as follows:

inverting the above transformation matrix to convert the Euler angular velocityAttitude angular velocity component omega in body coordinate system_ox，ω_oy，ω_ozTo show that:

c2, center of mass C and center of rotation O due to the upper station mechanism_o(i.e., body coordinate system (O)_o-X_oY_oZ_o) Origin O_o) The deviation exists between the rigid body posture kinematic and the rigid body posture kinematic of the upper station mechanism (3), so a calculation method after considering the deviation is given to the rigid body posture kinematic and the rigid body posture kinematic of the upper station mechanism:

set up barycenter C and rotation center O of station mechanism_oDeviation of r_cThe vector from the center of mass C to the origin of the inertial coordinate system isBody coordinate system (O)_o-X_oY_oZ_o) Origin O_oTo the inertial frame (O)_w-X_wY_wZ_w) The vector of origin isThe main vectors of all external forces acting on the upper station mechanism (3) areAll external forces are opposite to the rotation center O_oThe principal moment vector of a point isThe mass of the upper station mechanism is m_AThe mass of the lower station mechanism is m_PThe mass of the whole self-adaptive six-degree-of-freedom air floatation simulation test bed is M;

the rigid body model of the upper station mechanism is analyzed, and the following vector relationship is provided:

the derivative of the momentum of the upper station mechanism (3) to the time is equal to the main vector of the compressed air propulsion system, and the orbit dynamics equation of the upper station mechanism is obtained:

the upper station mechanism track dynamics formula can be expressed as:

in the above formula, F_pResultant of propulsive forces generated for compressed air propulsion systems, F_QThrust G generated by the first air floating ball bearing (9) to the upper station mechanism (3)_AIs the gravity and F borne by the upper station mechanism (3)_dThe working position mechanism (3) is subjected to external interference forces such as pneumatic interference and the like;

go up station mechanism (3) to O_oThe moment of momentum of the point is:

because any mass infinitesimal element and the spherical center O of the first air floating ball bearing_oThe following relationships exist between:

then go up station mechanism pair O_oThe moment of momentum of a point can be written as:

wherein the second term is that the upper station mechanism is aligned with the spherical center O of the first air floating ball bearing_oRelative moment of momentum of (a):

after the moment of momentum is derived over time, there are:

according to the definition of the vector cross product:the above formula can be written as:

since the external moment should be equal to the steelBody pair O_oThe derivative of the relative moment of momentum with time plus the rigid body addition moment to the origin, thus from the rigid body dynamic equilibrium formula, there is:

if introducing rigid body, rotating center O in body coordinate system_oTensor matrix J of moment of inertia_b：

The attitude dynamics equation of the upper station mechanism is as follows:

whereinFor external moment, including air propulsion of compressed air propulsion systems (f)₁～f₄) The generated control moment, the gravity center and the rotation center O of the upper station mechanism_oMoments generated by misalignment, aerodynamic damping moments, and eddy currents moments.

Drawings

FIG. 1 is a front view of an adaptive six-degree-of-freedom air-bearing simulation test bed according to the first embodiment.

FIG. 2 is a main sectional view of the adaptive six-degree-of-freedom air-floating simulation test bed according to the first embodiment.

FIG. 3 is a schematic diagram of an adaptive six-degree-of-freedom air-floating simulation test bed according to the first embodiment.

FIG. 4 is a cross-sectional view of an adaptive air bearing assembly according to an embodiment.

FIG. 5 is a diagram illustrating a state of use of an adaptive air bearing set according to an embodiment.

Fig. 6 is a schematic diagram of an adaptive air-floating platform set composed of three adaptive six-degree-of-freedom air-floating simulation test beds in the first embodiment.

FIG. 7 is a schematic diagram of a coordinate system of a porous medium ball bearing derived in the first embodiment.

FIG. 8 is a schematic view of a porous medium ball bearing according to one embodiment.

FIG. 9 is a schematic diagram of deriving the thickness of the gas film in the first embodiment.

FIG. 10 shows an inertial frame (O) according to the first embodiment_w-X_wY_wZ_w) With body coordinate system (O)_o-X_oY_oZ_o) Schematic representation.

Fig. 11 is a schematic view of an euler angle transformation relationship between an inertial coordinate system and a body coordinate system according to an embodiment.

FIG. 12 is a schematic vertical statics diagram of the adaptive six-degree-of-freedom air-floating simulation test bed according to the first embodiment.

Fig. 13 is a diagram illustrating a posture motion analysis of the upper stage mechanism according to the first embodiment.

In the figure: 1. the test bed comprises a test bed, 2, a lower station mechanism, 3, an upper station mechanism, 4, a lower station platform, 5, a lifting support, 6, a lifting driving mechanism, 7, an air floating journal bearing, 8, a first air floating plane bearing, 9, a first air floating ball bearing, 10, an adaptive air floating group, 11, an adaptive support, 12, a second air floating plane bearing, 13, a second air floating ball bearing, 14, a first high-pressure air tank, 15, a first air passage, 16, a second high-pressure air tank, 17, a second air passage, 18, a supporting plate, 19, a sphere, 20, an air film, 21, a porous medium, 22, an air cavity, 23 and a compressed air propeller.

Detailed Description

The following examples are further illustrative of the present invention, but the present invention is not limited thereto. The present invention is relatively complicated, and therefore, the detailed description of the embodiments is only for the point of the present invention, and the prior art can be adopted for the present invention.

The first embodiment is as follows:

fig. 1 to 13 show a first embodiment of the present invention.

As shown in fig. 1, the adaptive six-degree-of-freedom air-flotation simulation test bed comprises a test bed 1, a lower station mechanism 2 and an upper station mechanism 3.

As shown in fig. 2, the lower station mechanism 2 includes a lower station platform 4, a lifting bracket 5, a lifting driving mechanism 6, an air floating journal bearing 7, a first air floating plane bearing 8, a first air floating ball bearing 9, a first air supply module, and an adaptive air floating group 10.

The lifting support 5 is mounted on the lower station platform 4 through an air-floating journal bearing 7, and the air-floating journal bearing 7 has one degree of freedom of movement and one degree of freedom of rotation (see fig. 3), so that the lifting support 5 can vertically move and rotate around a vertical shaft relative to the lower station platform 4.

The lifting driving mechanism 6 is used for driving the lifting bracket 5 to vertically move relative to the lower station platform 4. The first air bearing 8 is provided between the lift drive mechanism 6 and the lift bracket 5, and the first air bearing 8 has a rotational degree of freedom such that the lift bracket 5 can rotate about a vertical axis with respect to the lift drive mechanism 6 (see fig. 3). Specifically, as shown in fig. 2, the lifting driving mechanism 6 is a linear motor, the linear motor is mounted on the lower station platform 4, a rotor of the linear motor is connected with the supporting plate 18, and the first air-bearing plane bearing 8 is arranged between the supporting plate 18 and the lifting support 5.

The lifting support 5 is connected with the station loading mechanism 3 through a first air floating ball bearing 9, and the station loading mechanism 3 is used for installing a satellite control system. The first air ball bearing 9 has three rotational degrees of freedom (see fig. 3), so that the upper station mechanism 3 can rotate freely relative to the lifting bracket 5.

The first air supply module is used for supplying air for lubricating the air floating journal bearing 7, the first air floating plane bearing 8 and the first air floating ball bearing 9. Specifically, first air feed module includes first high-pressure gas pitcher 14 and first gas duct 15, first high-pressure gas pitcher 14 is installed under on station platform 4, station platform 4 is down located in first gas duct 15, first high-pressure gas pitcher 14 is connected with air supporting journal bearing 7, first air supporting plane bearing 8, first air supporting ball bearing 9 respectively through first gas duct 15.

As shown in FIG. 1, the adaptive air flotation groups (10) are provided with three groups and are arranged at the bottom of the lower station platform 4 at intervals of 120 degrees along the same circumference. As shown in fig. 4, the adaptive air-floating group (10) includes an adaptive bracket 11, a second air-floating plane bearing 12, and a second air-floating ball bearing 13. The second air supply module is connected with the second air bearing 12 and the second air ball bearing 13 through a second air passage 17 and supplies air to the second air bearing 12 and the second air ball bearing 13.

The second air bearing 12 is installed between the adaptive bracket 11 and the test bed 1, and the second air bearing 12 has two degrees of freedom of movement, so that the adaptive bracket 11 can move horizontally relative to the test bed 1.

The adaptive support 11 is connected with the lower station platform 4 through a second air ball bearing 13, and the second air ball bearing 13 has three rotational degrees of freedom, so that the lower station platform 4 can rotate freely relative to the adaptive support 11 (as shown in fig. 5), and the adaptive support 11 can be kept in a parallel state with the test bed 1 in a self-adaptive manner.

The second air supply module is used for supplying air for lubrication to the second air bearing 12 and the second air ball bearing 13. Specifically, the second air supply module comprises a second high-pressure air tank 16 and a second air flue 17, the second high-pressure air tank 16 is installed on the self-adaptive support 11, the second air flue 17 is arranged in the self-adaptive support 11), and the second high-pressure air tank 16 is respectively connected with the second air-floatation plane bearing 12 and the second air-floatation ball bearing 13 through the second air flue 17. The second high-pressure gas tanks 16 are provided in plurality and are uniformly distributed in the same circumferential direction. The center of mass of each adaptive air-floating group 10 can be coincided with the resultant force center of the air buoyancy of the second air-floating plane bearing and is vertically upward. Each adaptive air flotation group 10 is also provided with a fine adjustment device for the center of gravity.

As shown in fig. 5, when the plane of the test bed 1 below the adaptive air-bearing group 10 has local unevenness, the reaction force at the end with reduced thickness on the air film of the second air-bearing plane 12 increases, and the reaction force at the end with increased thickness decreases, so as to generate a counteracting moment. This moment will cause the adaptive support 11 to adaptively maintain parallelism relative to the plane of the test stand 1.

The adaptive air-floating groups 10 in this embodiment are provided with three groups and are arranged at intervals of 120 ° along the same circumference at the bottom of the lower station platform 4 (see fig. 1), so that the influence of the unevenness of the plane of the test bed 1 is a statistical average value rather than a maximum value, which affects the lateral force of the system. Therefore, the requirement for the unevenness of the whole test bed 1 plane can be decomposed into the requirement for the local unevenness in a differential mode, the processing difficulty of the test bed 1 is greatly reduced, and the possibility is provided for the test with larger scale.

The upper station mechanism 3 is provided with a compressed air propulsion system which comprises four compressed air propellers 23 uniformly distributed along the circumferential direction of the upper station mechanism 3.

The six degree of freedom air supporting emulation test benches of self-adaptation that this embodiment provided has used four air supporting plane bearings (a first air supporting plane bearing 8 and three second air supporting plane bearing 12), four air supporting ball bearing (a first air supporting ball bearing 9 and three second air supporting ball bearing 13) and an air supporting journal bearing 7, makes six degree of freedom air supporting emulation test benches of self-adaptation can be similar to have not friction, carry out various motions on the large-scale test bench 1 plane in ground with low interference, include: 1) the lower working mechanism 2 is self-adaptively kept parallel to the plane of the test bed 1; 2) the lower station platform 4 realizes X, Y, Z linear orbital motion in three directions; 3) the upper station mechanism 3 is supported on the lower station mechanism 2 through a first air floating ball bearing 9 and can do rotary attitude motion around a transverse rolling shaft, a pitching shaft and a yawing shaft.

Therefore, the self-adaptive six-degree-of-freedom air floatation simulation test bed of the embodiment can simulate the space task of the combined action of the spacecraft orbit and the attitude under the ground environment, and is the full physical simulation of the self-adaptive six-degree-of-freedom air floatation simulation test bed, including the kinematics and dynamics of the position and the attitude; attitude control and image recognition; controlling a sliding mode variable structure; and a plurality of adaptive six-degree-of-freedom air-flotation simulation test bed formations and the like provide equipment and means for testing (figure 6).

In order to simplify the processing, improve the bearing and reduce the flow, all the air bearings (an air bearing journal bearing 7, a first air bearing plane bearing 8, a first air bearing ball 9, a second air bearing plane bearing 12 and a second air bearing ball bearing 13) in the self-adaptive six-degree-of-freedom air bearing simulation test bed adopt a porous medium throttling mode. Because the porous medium throttling air bearing has higher bearing rigidity, bearing capacity and damping characteristic under the conditions of effective air supply area and air supply pressure, the porous medium throttling air bearing is taken as a calculation example in the embodiment. Although there are similar algorithms for the orifice and slit throttle air bearings, the patent is not repeated.

In the calculation of the porous medium air bearing, various methods such as a Darcy method, a bearing factor method, an equivalent gap model method, a fractal theory method and the like have been developed. In this embodiment, the main purpose is to obtain a basic performance estimate, serving the purpose of the present invention. Thus, the present embodiment still uses the conventional method. Namely: the porous medium is regarded as a uniform porous body, a Reynolds equation in a spherical clearance of the air-floating ball bearing and a Darcy equation in the porous medium are combined, the rotating speed of the air-floating ball bearing is assumed to be zero, then the edge value problem of the equations is solved through a difference method discretization, the surface pressure of the air-floating ball bearing is obtained, and further parameters such as the bearing capacity of the air-floating ball bearing are obtained through integration.

According to the inventive concept, a spherical coordinate system Or θ φ is established for this purpose, which is shown in FIGS. 7-9 in relation to the original XYZ coordinates and orientation positioning. The air-float ball bearing parameters are as follows: r is the radius of the sphere 19, theta₀Is the bearing wrap angle, and h is the bearing average gas film 20 thickness.

The pressure distribution of the spherical surface of the sphere 19 can be obtained by calculating the fluid mechanics, and the bearing capacity of the porous medium air-float ball bearing can be obtained by integration.

For example, if the diameters of the first air ball bearing 9 and the second air ball bearing 13 are 270mm and 54mm, respectively, the average thickness of the air film 20 is 0.03mm, the porous medium is made of 320 mesh bronze powder by sintering, and the sintered air film is processed by a diamond cutter, ground and molded, the sphericity is controlled to be about 1 micron, the air supply pressure is 0.4mpa, and the bearing capacities are not less than 2500N and not less than 500N, respectively, by preliminary calculation. Because the lower part of the lower station mechanism 2 is provided with three self-adaptive air flotation groups 10, and each self-adaptive air flotation group 10 is provided with one second air flotation ball bearing 13, the whole lower station platform 4 is supported by the three second air flotation ball bearings 13 at the lower part, and the total bearing capacity is about 1500N.

In view of the isolation of the air tank on the self-adaptive six-degree-of-freedom air floatation simulation test bed from the outside, in order to enable the self-adaptive six-degree-of-freedom air floatation simulation test bed to work for a long time, it is an important factor to reduce the flow of the air floatation bearing as much as possible on the premise of ensuring the bearing capacity. For the porous medium air bearing, the analysis can be approximately carried out by using the airflow flow between two parallel plates, and the following equation is provided:

in the formula P_d，P_aRespectively, the inlet of the compressed air source and the atmospheric pressure, D is the perimeter of the outlet, h_oThe thickness of the air film 20 is l, the air path length of the air ball bearing. It can be seen that the gas flow rate is proportional to the cube of the thickness of the air film 20 of the air ball bearing. This is important in view of the extended platform operating time, since only a small increase in clearance results in a significant increase in gas flow and a steep decrease in operating time.

The self-adaptive six-degree-of-freedom air floatation simulation test bed also needs to model the kinematics and dynamics models of the position and the posture of the self-adaptive six-degree-of-freedom air floatation simulation test bed. The prior art documents have only five degrees of freedom at most, namely two degrees of freedom for planar movement and three degrees of freedom for rotation. This patent proposes six degrees of freedom, three degrees of freedom for linear movement and three degrees of freedom for rotation. Therefore, in this embodiment, the displacement and attitude conversion relationship, the kinematics and the kinetic equation of the six-degree-of-freedom air-floating simulation test bed need to be given, so as to lay a foundation for the position and attitude measurement and control using the invention.

For this purpose, two coordinate systems are established (as shown in fig. 10): one is an inertial frame (O) fixed to the ground_w-X_wY_wZ_w) (ii) a The other is a body coordinate system (O)_o-X_oY_oZ_o)。

Thus, the spatial state (position) of the upper station mechanism (3)And attitude) can be determined from the body coordinate system (O)_o-X_oY_oZ_o) Origin O_oIn the inertial frame (O)_w-X_wY_wZ_w) Is added with three euler angle conversions between the two coordinate axes (see fig. 11). First around Z_OThe axis being rotated through an angle psi (yaw angle) and then about Y_O1Shaft rotation angle θ (pitch angle); finally wound around X_O2The shaft is rotated by an angle phi (roll angle). Under such an arrangement, a body coordinate system (O)_o-X_oY_oZ_o) Can be converted into an inertial coordinate system (O) by a coordinate transformation method_w-X_wY_wZ_w) Vector R in (2):

R_i＝[T]R′_i+P i＝1,2,…,6

in the formula [ T]Is a direction cosine matrix of the attitude (three coordinate axes) of the body coordinate system on the inertial coordinate system. Three rows of which are three axes X of the body coordinate system respectively_o，Y_oAnd Z_oDirection cosine in the inertial frame.

P is the origin O of the body coordinate system_oCoordinate values on the inertial coordinate system.

p＝{X₀ Y₀ Z₀}

The transfer matrix T is a transfer matrix from the inertial coordinate system to the body coordinate system. If only azimuthal variations (pitch angle θ, yaw angle ψ, and roll angle φ) are considered, the above transfer matrix T can be written as the product of three elementary rotation matrices:

in the above formula, c and s are abbreviations for cos and sin, respectively, as follows. In the formula, phi, theta, psi may be constant, or may be any function of time phi (t), theta (t), psi (t).

When the adaptive six-degree-of-freedom air-flotation simulation test bed moves, the six parameters (three original coordinates and three azimuth angles) can be expressed as a single-value continuous function of time, namely, an adaptive six-degree-of-freedom air-flotation simulation test bed kinematic equation:

x is above₀(t),y₀(t),z₀(t) the derivative with respect to time in the inertial frame is the velocity of the origin of the body frame

For the attitude motion, as mentioned above, the rotation of the upper station mechanism 3 and the body motion coordinate system fixed thereon relative to the inertial coordinate system is respectively completed around three axes at the euler angular velocity, and the vector sum thereof is the resultant angular velocity of the rotation of the upper station mechanism 3. This resultant angular velocity vector ω is expressed in terms of euler angular velocity, and is then:

wherein ω is_ox，ω_oy，ω_ozThe three angular velocity components can be measured by a gyroscope fixedly connected in the body coordinate system on the upper station mechanism 3. Similarly, the coordinate array of Euler angular velocities and three Euler angular velocities in the body coordinate system The relationship of (A) can be:

inverting the transformation matrix in the formula, that is, expressing the euler angular velocity in the mathematically non-orthogonal coordinate system by the attitude angular velocity component in the body coordinate system:

the final purpose of the invention is to provide measurement and control basis for the position and the posture of the self-adaptive six-degree-of-freedom air floatation simulation test bed. Therefore, as the content of the invention, a related calculation method is also needed to be provided for the dynamic characteristics of the adaptive six-degree-of-freedom air floatation simulation test bed.

The motion of the self-adaptive six-degree-of-freedom air floatation simulation test bed consists of two parts: the orbital motion of the lower station mechanism 2 and the orbital motion and the attitude motion of the upper station mechanism 3. Therefore, the kinetics of these two parts need to be handled separately.

The orbital motion of the lower station mechanism 2 includes a body coordinate system (O) placed on the lower station mechanism 2_o-X_oY_oZ_o) Origin O_oInertial coordinate system (O) on test stand 1_w-X_wY_wZ_w) Planar movement and up and down movement perpendicular to the plane of the test stand 1. These movements determine the origin position of the upper station mechanism 3.

Body coordinate system (O) placed on lower station mechanism 2_o-X_oY_oZ_o) Origin O_oInertial coordinate system (O) on test stand 1_w-X_wY_wZ_w) The vertical movement is controlled by a lift drive mechanism 6. And a body coordinate system (O)_o-X_oY_oZ_o) Origin O_oInertial coordinate system (O) on test stand 1_w-X_wY_wZ_w) Can be easily determined from the following equation, for example, for X_wThe directions are as follows:

the movement of the upper station mechanism 3 comprises two parts of orbital linear movement and attitude rotation (see fig. 1-3). When in work, the station loading mechanism 3 not only generates orbital linear motion (orbital motion) relative to an inertial coordinate system along with the body coordinate system, but also generates orbital linear motion (orbital motion) around the spherical center O of the first air floating ball bearing 9 along with the body coordinate system_oThe rotational movement is made at an angular speed of omega (see figure 8). Under ideal working conditions, the mass center C of the upper station mechanism 3 needs to be adjusted to be equal to the rotation center O_oAnd overlapping, thereby simulating the situation of weightlessness in the outer space. In practice, however, it is difficult to achieve absolute registration, and there is a certain deviation between the two (see fig. 13). This needs to be corrected in view of the attitude rotation.

As can be seen from fig. 13, the working position loading mechanism 3 follows the body coordinate system and is relative to the inertial coordinate system (O)_w-X_wY_wZ_w) Doing horizontal and vertical movement and surrounding the spherical center O of the first air floating ball bearing along the body coordinate system_oRotating at an angular speed of omega. Set up barycenter C and rotation center O of station mechanism 3_oDeviation of r_c. The vector from the centroid C point to the origin of the inertial coordinate system isThe vector from the origin of the body coordinate system to the origin of the inertial coordinate system isThe main vector of all external forces acting on the upper station mechanism 3 isAll external forces are opposite to the rotation center O_oThe principal moment vector of a point isThe upper station mechanism 3 has the mass m_AThe lower station mechanism 2 has the mass m_PThe mass of the whole self-adaptive six-degree-of-freedom air floatation simulation test bed is M. Considering that the lower station mechanism 2 only moves horizontally and vertically along the plane of the test bed 1, only the upper station mechanism 3 has rotation around the rotation center. To the upper station mechanism 3The rigid body model is analyzed, and the following vector relationship is provided:

since the derivative of the momentum of the upper station mechanism 3 to time is equal to the main vector of the compressed air propulsion system, the orbit dynamics equation of the upper station mechanism 3 can be obtained:

as can be seen from the force analysis in FIG. 12, the external force applied to the upper working mechanism 3Mainly divided into propulsion F produced by compressed-air propulsion systems_pThe thrust F generated by the air film 20 (see figure 7) of the first air floating ball bearing 9 to the upper station mechanism 3_QThe upper station mechanism 3 bears the gravity G_AAnd the external interference force F such as pneumatic interference of the upper station mechanism 3_d(see FIG. 12). The track dynamics formula of the upper station mechanism 3 can be expressed as:

the derivation result of the attitude motion dynamics of the upper station mechanism 3 is described as follows:

go up station mechanism 3 to O_oThe moment of momentum of the point is:

because of any mass infinitesimal and the spherical center O of the first air floating ball bearing 9_oThe following relationships exist between:

then the upper station mechanism (3) is paired with O_oThe moment of momentum of a point can be written as:

the second item is the center O of the first air floating ball bearing 9 of the upper station mechanism 3_oRelative moment of momentum of (a):

after the moment of momentum is derived over time, there are:

according to the definition of the vector cross product:the above formula can be written as:

because the external moment should be equal to the rigid body pair O_oThe derivative of the relative moment of momentum with time plus the rigid body addition moment to the origin, thus from the rigid body dynamic equilibrium formula, there is:

if introducing rigid body, rotating center O in body coordinate system_oTensor matrix J of moment of inertia_b：

The attitude dynamic equation of the upper station mechanism (3) is as follows:

whereinFor external moment, including compressed-air propellers 23 (f)₁～f₄) The generated control moment, the gravity center and the rotation center O of the upper station mechanism 3_oMoment generated by misalignment, aerodynamic damping moment, eddy moment and the like.

The present invention has been described in detail above with reference to specific embodiments thereof and general description. These aspects include: 1) self-adaptive adjustment of a self-adaptive six-degree-of-freedom air floatation simulation test bed; 2) realizing six-degree-of-freedom motion of the self-adaptive six-degree-of-freedom air floatation simulation test bed; 3) designing, calculating and considering the technology of an air bearing (especially a porous medium air bearing) of a self-adaptive six-degree-of-freedom air bearing simulation test bed; 4) the rail dynamics of the lower station mechanism 2; 5) the track dynamics and the attitude dynamics of the upper station mechanism 3, and the like.

Although the invention has been described in detail herein with reference to specific embodiments and examples, it will be apparent to one skilled in the art that certain changes and modifications can be made therein without departing from the spirit and scope of the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.